Combinatorial Route to Algebra: The Art of Composition & Decomposition
Pawel Blasiak
Abstract
We consider a general concept of composition and decomposition of
objects, and discuss a few natural properties one may expect from a
reasonable choice thereof. It will be demonstrated how this leads to
multiplication and co-multiplication laws, thereby providing a generic
scheme furnishing combinatorial classes with an algebraic
structure. The paper is meant as a gentle introduction to the concepts
of composition and decomposition with the emphasis on combinatorial
origin of the ensuing algebraic constructions.
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